First- and Second-Order Piezoresistive Coefficients of CMOS FETs From Strong Into Weak Inversion

For many years, researchers have noted that the stress response of MOS transistors exhibits strong deviations from a pure mobility behavior as the devices exit strong inversion, but there has been no easily accessible stress model that sensor designers can use in the design of their devices. In this work, generalized piezoresistance coefficients are presented that provide continuous modeling of the stress dependencies of CMOS FETs from weak into strong inversion. The models presented here incorporate both standard mobility variations plus the additional impact of threshold voltage changes on the stress responses in all regions of operation. The theory predicts both first- and second-order longitudinal and traverse piezoresistive coefficients for PMOS and NMOS devices that are verified with experimental results. The threshold voltage variations represent common-mode terms, so orthogonal differential pairs of MOSFETs can still be utilized to directly measure the important mobility components of the overall stress response, and the impact of the threshold voltage terms on sensor circuits may be reduced with differential design.